Title: Apr 26-10:30 PM (1 of 13)

So. What Can You Do With a SmartBoard?

Introducing ... The Book ...

Title: Apr 26-11:05 PM (2 of 13)

Come write your name ... anyone, c'mon give it a try. It won't hurt ... really ...

Jennifer

Title: Apr 27-8:56 AM (3 of 13)

A Sample Lesson ...

... before ...

... during ...

... and after ...

*

Title: Apr 27-8:51 AM (4 of 13)

The Binomial Theorem

Zhu Shijiei 1261

Pascal 1653

or "one of the ways G-d built the universe" ...

Title: Apr 27-3:01 PM (5 of 13)

ANNOTATE THIS

Title: Apr 27-8:52 AM (6 of 13)

Expand and simplify ...

a + b

Title: Apr 27-8:52 AM (7 of 13)

1

Find a pattern, add two more rows to the triangle ...

1 11 2 1

1 3 3 11 4 6 4 1

Title: Apr 27-8:52 AM (8 of 13)

Evaluate each term ...

Title: Apr 27-8:52 AM (9 of 13)

Pascal's TriangleHow many different patterns can you find in the triangle?

SYMMETRY

Sum of COUNTING numberstriangular numbers

Counting Numbers

Sum of Triangular numbers

Title: Apr 27-8:52 AM (10 of 13)

Pascal's TriangleHow many different patterns can you find in the triangle?

Title: Apr 27-8:53 AM (11 of 13)

Pascal's TriangleHow many different patterns can you find in the triangle?

Title: Apr 27-8:53 AM (12 of 13)

Title: Apr 27-8:53 AM (13 of 13)

The Binomial Theorem ...

Algebraically

Combinatorically

Notice the patterns ...(1) The coefficient of the term is: (2) The exponent on a is given by: [n - (i - 1)](3) The exponent on b is given by: i(4) This relation holds for each term in the expansion: [exponent on a] + [exponent on b] = n(5) The number of terms in any binomial expansion is: n + 1